# A large box of mass M is pulled across a horizontal frictionless surface by a horizontal rope with tension T.A small box of mass m sits on top of the large box. The coefficients of static and...

A large box of mass M is pulled across a horizontal frictionless surface by a horizontal rope with tension T.

A small box of mass m sits on top of the large box. The coefficients of static and kinetic friction between the two boxes are mu_s (static friction) and mu_k (kinetic friction) respectively. Find an expression for the maximum tension Tmax for which the small box rides on top of the large box without slipping.

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### 1 Answer

You should use the equation that relates the frictionn force and normal force such that:

`F_f = mu_s*N`

You need to remember that you may substitute `N = G = m*g` such that:

`F_f = mu_s*(m*g)`

You need to evaluate the friction force using the Newton's second law such that:

`m*a = mu_s*(-m*g) => a = mu_s*g`

You should evaluate the maximum tension for which the small box rides on top of the large box without slipping such that:

`T = (M+m)*a => T = mu_s*g*(M+m)`

**Hence, evaluating the maximum tension for which the small box rides on top of the large box without slipping and using a coefficient of static friction yields `T = mu_s*g*(M+m).` **